As algorithmic (and particularly machine learning) decision making systems become both more widespread and make more important decisions, there are growing concerns about their embedded values and ability to establish legitimacy among decision subjects. We argue that designing for contestability in these systems can assist in surfacing values, aligning system design and use with context, and building legitimacy. However, designing for contestability can be challenging, particularly in systems that are designed to be opaque: systems need to accurately surface embedded values, expose decision making processes in ways that are meaningful for users, support engagement with and allow influence over system performance, and so on. In addition to these technical aspects, designing for contestability may by challenged by the need to protect intellectual property and prevent gaming of the system. In this workshop, we will address goals, audiences, and designs for contestability in algorithmic systems. We hope to develop a taxonomy of contestable systems and understand the value provided by contestability, while bringing together a community to work on this multidisciplinary problem.